A sector is a part of a circle cut by two of the circles radii and an arc. The following figure shows an example of a sector. In real life, pizza slices are a perfect example of a sector.
The length of the arc can be determined if you know the angle the sector subscribes at the center (angle 
shown in the above figure). The area of the sector is determined using the following formula:
shown in the above figure). The area of the sector is determined using the following formula:
Sector Area 
You can easily derive the area if you understand that the area of the sector is directly proportional to the angle subscribed at the center. By now you know that the angle subscribed by the circle at the center is 360°. In effect the entire circle is one giant sector with angle 360° at the center.
Area of circle with angle 360° subscribed at the center 
Area of sector with angle subscribed at the center 
subscribed at the center 
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